Tool and Object

A History and Philosophy of Category Theory

  • Ralf Krömer

Part of the Science Networks. Historical Studies book series (SNHS, volume 32)

About this book


The book is first of all a history of category theory from the beginnings to A. Grothendieck and F.W. Lawvere. Category theory was an important conceptual tool in 20th century mathematics whose influence on some mathematical subdisciplines (above all algebraic topology and algebraic geometry) is analyzed. Category theory also has an important philosophical aspect: on the one hand its set-theoretical foundation is less obvious than for other mathematical theories, and on the other hand it unifies conceptually a large part of modern mathematics and may therefore be considered as somewhat fundamental itself. The role of this philosophical aspect in the historical development is the second focus of the book. Relying on the historical analysis, the author develops a philosophical interpretation of the theory of his own, intending to get closer to how mathematicians conceive the significance of their activity than traditional schools of philosophy of science.

The book is the first monography exclusively devoted to the history of category theory. To a substantial extent it considers aspects never studied before. The author uses (and justifies the use of) a methodology combining historical and philosophical approaches. The analysis is not confined to general remarks, but goes into considerable mathematical detail. Hence, the book provides an exceptionally thorough case study compared with other works on history or philosophy of mathematics. The philosophical position developed here (inspired by Peircean pragmatism and Wittgenstein) is an interesting alternative to traditional approaches in philosophy of mathematics like platonism, formalism and intuitionism.


Algebra Grothendieck, Alexander History of Mathematics Homological algebra Mac Lane, Saunders category theory epistemology

Authors and affiliations

  • Ralf Krömer
    • 1
  1. 1.LPHS-Archives Poincaré (UMR7117 CNRS)Université Nancy 2Nancy CedexFrance

Bibliographic information

  • DOI
  • Copyright Information Birkhäuser Verlag AG 2007
  • Publisher Name Birkhäuser Basel
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-7643-7523-2
  • Online ISBN 978-3-7643-7524-9
  • About this book